# Total inversion

Author: mathforces
Problem has been solved: 31 times

Русский язык | English Language

We call a finite set $S$ of points in the plane strange if for every point $P$ in $S$, we can find an inversion with respect to a circle of some radius with center at $P$ which maps every point in $S$ distinct from $P$ to another point in $S$ (possibly the same point). Find the largest possible size of a strange set not contained in any line.